Question: Factor the following expression: $27x^2 - 75$
Explanation: We can start by factoring a ${3}$ out of each term: $ {3}({9x^2} - {25})$ The second term is of the form ${a^2} - {b^2}$ , which is a difference of two squares so we can factor it as ${3}({a} + {b}) ({a} - {b})$ What are the values of $a$ and $b$ $ a = \sqrt{9x^2} = 3x$ $ b = \sqrt{25} = 5$ Use the values we found for $a$ and $b$ to complete the factored expression, ${3}({a} + {b}) ({a} - {b})$ So we can factor the expression as: ${3}({3x} + {5}) ({3x} - {5})$